Merge pull request #77 from Rudra-IITM/work1

[Add] Monotone-Chain Algorithm for Convex-Hull

Computational_Algorithms/Hull/monotone_chain_algo.cpp

@@ -0,0 +1,72 @@
+// Convex Hull --> Smallest convex set which encloses all points in it
+
+#include<bits/stdc++.h>
+using namespace std;
+
+// Custom Data Structure to store points in 2D palne
+struct point{
+	float x, y;
+	point () { x=0,y=0;}
+	point(float x1, float y1) {x=x1, y=y1;} 
+};
+
+// Custom comparator for point DS
+bool comp(point &p1, point &p2){
+	if(p1.x!=p2.x) return p1.x<p2.x;
+	return p1.y<p2.y;
+}
+
+// Calculating orientation of given points using area
+int cw(point &a, point &b, point &c){
+	double area=a.x*(b.y-c.y) + b.x*(c.y-a.y) + c.x*(a.y-b.y);
+	if (area<0) return 1;
+    else if (area==0) return 2;
+    return 3;
+}
+
+vector<point> convex_hull(vector<point> &v){
+	if(v.size()==1) return v;
+	// Sort given points according to their abscissa (and ordinate in case of tie)
+	sort(v.begin(), v.end(), comp);
+	point p1=v[0], p2=v.back();
+
+	// Intialise up and down DS to store upper and lower convex hull
+	vector<point> up, down;
+	up.push_back(p1);
+	down.push_back(p1);
+
+	for(long unsigned int i=1;i<v.size();i++){
+		// If current point is a valid point for upper hull
+		if(i==v.size()-1 || cw(p1, v[i], p2)==1){
+			while(up.size()>=2 && cw(up[up.size()-2], up[up.size()-1], v[i])>1)
+				up.pop_back();
+			up.push_back(v[i]);
+		}
+
+		// If current point is a valid point for lower hull
+		if(i==v.size()-1 || cw(p1, v[i], p2)==3 ){
+			while(down.size()>=2 && cw(down[down.size()-2], down[down.size()-1], v[i])<3)
+				down.pop_back();
+			down.push_back(v[i]);
+		}
+	}
+
+	// Merge both upper and lower hull to get final points in Hull
+	for(long unsigned int i=down.size()-2;i>0;i--) up.push_back(down[i]);
+	return up;
+}
+
+int main(){
+    int n;
+    cin>>n;
+    vector<point> v;
+    while(n--){
+        float x,y;
+        cin>>x>>y;
+        point p=point(x,y);
+        v.push_back(p);
+    }
+    vector<point> hull=convex_hull(v);
+    cout<<hull.size()<<endl;
+    for (auto it:hull) cout<<(long long int)it.x<<" "<<(long long int)it.y<<endl;
+}